•Reliability-based assessment of the post-fire residual capacity of a concrete slab.•Comprehensive methodology introduced through application to a real-life case study.•Information obtained through ...inspections, tests, and modelling can be combined.•Only existing simplified method for reliability-based post-fire assessment.•The proposed methodology can be easily applied by practicing engineers.
For most fires occurring in buildings with a concrete structural frame, the structural elements do not collapse during fire exposure, and further use of the building after fire may be possible. Fire can nevertheless result in a permanent loss of strength and thus a post-fire evaluation of the residual load bearing capacity has to be made to inform decisions on continued use and the need for structural repairs. This evaluation is however particularly difficult due to the many uncertainties associated with both the fire exposure and the characteristics of the structural elements. These uncertainties cannot be neglected when determining the residual capacity since adequate safety is a major societal concern as indicated by the predominance of safety in current design standards and guidance documents. In this paper a comprehensive methodology is presented for the assessment of the residual capacity of concrete structures after exposure to fire. The methodology is introduced through application to a real-life case study of an apartment fire with a focus on the end-span of the affected continuous concrete slab. It results in a reliability-based evaluation of the maximum allowable characteristic value for the imposed load on the slab. The presented methodology is useful to make informed decision about continued use of structures after a fire event.
•Comparison of evaluation methods for RC slab subject to column removal scenarios.•Tensile membrane action effects taken into account.•Energy-Based Method predicts maximum dynamic responses ...accurately.•Strain rate effect, damping, and column removal duration investigated.•Model uncertainty when using the energy-based method quantified.
The Alternative Load Path (ALP) method is widely used to assess progressive collapse resistance of reinforced concrete (RC) structures by notional removal of one or more load-bearing elements. In general, a nonlinear time history analysis (NTHA) is needed to perform such an analysis if dynamic effects are explicitly taken into account. To avoid cumbersome nonlinear dynamic analyses, the energy-based method (EBM) is a promising technique to predict the maximum dynamic responses of a structural system. In this article, the accuracy and precision of the EBM is evaluated based on a validated finite element model of a tested RC slab subjected to a sudden column removal scenario, in particular in relation to the investigation of tensile membrane action (TMA). Influences of dynamic effects are evaluated, i.e. in relation to strain rate effects, damping, and the time duration of support removals. Strain rate effects are observed to have only slight influences on the dynamic responses. The strain rate dependency of reinforcement is found to have a more significant influence on the responses in TMA stage, although also to a limited extent. The magnitude of the load has a significant influence on the dynamic response, as do increasing damping ratios due to the corresponding significant energy dissipation. Finally, the dynamic response reduces with increasing time duration of the column removal. Based on the results of the stochastic analyses, the EBM is observed to perform well based on a comparison with the results of NTHA in both flexural and TMA stages. Furthermore, in relation to the analyzed case studies on reinforced concrete slabs, the model uncertainty of the responses obtained through the EBM compared with the NTHA is found to be represented well by a lognormal distribution with mean of 0.95 and a standard deviation of 0.20, for evaluating the loads of first rupture of reinforcement. Furthermore, a lognormal distribution with mean 0.96 and standard deviation 0.13 is found appropriate to represent the model uncertainty on ultimate load-bearing capacity predictions. Model uncertainties are also obtained with respect to the model predictions for displacements at the moment of the first rupture of reinforcement, displacements at the ultimate load-bearing capacities, and both loads and displacements at second load peaks.
The interest in probabilistic methodologies to demonstrate structural fire safety has increased significantly in recent times. However, the evaluation of the structural behavior under fire loading is ...computationally expensive even for simple structural models. In this regard, machine learning-based surrogate modeling provides an appealing way forward. Surrogate models trained to simulate the behavior of structural fire engineering (SFE) models predict the response at negligible computational expense, thereby allowing for rapid probabilistic analyses and design iterations. Herein, a framework is proposed for the probabilistic analysis of fire exposed structures leveraging surrogate modeling. As a proof-of-concept a simple (analytical) non-linear model for the capacity of a concrete slab and an advanced (numerical) model for the capacity of a concrete column are considered. First, the procedure for training surrogate models is elaborated. Subsequently, the surrogate models are developed, followed by a probabilistic analysis to evaluate the probability density functions for the capacity. The results show that fragility curves developed based on the surrogate model agree with those obtained through direct sampling of the computationally expensive model, with the 10
–2
capacity quantile predicted with an error of less than 5%. Moreover, the computational cost for the probabilistic studies is significantly reduced by the adoption of surrogate models.
A probabilistic risk assessment (PRA) is commonly accepted as a tool for performance based design in fire safety engineering, but the position of PRA in the design process, the relationship between ...different acceptance concepts (absolute, comparative, ALARP), and the responsibilities of the designer remain unclear. Aiming to clarify these aspects, the safety foundation of fire safety solutions is investigated, indicating that PRA is necessary for demonstrating adequate safety when no appeal can be made to the collective experience of the profession. It is suggested that PRA is not a methodology for ‘future fire safety engineering’, but rather a necessary methodology to provide an objective safety foundation for uncommon fire safety designs. Acknowledging that what constitutes ‘acceptable safety’ is subjective and may change over time, an objective proxy of ‘adequate safety’ is defined and proposed as a benchmark against which to assess the adequacy of fire safety designs. In order to clarify the PRA process, a hierarchy of different acceptance concepts is presented. Finally, it is shown how, depending on the applied acceptance concepts, the designer takes responsibility for different implicit assumptions regarding the safety performance of the final design.
AbstractStructural risk assessment against fire requires robust material models that take into account the uncertainty in material behavior over a range of elevated temperatures. Such probabilistic ...material models can directly inform performance-based design procedures for building fire safety. The objective of this research is to quantify uncertainties in retained strengths of steel and concrete when exposed to fire. First, hundreds of experimental data points covering a temperature range of 20°C–1,000°C are collected from literature. Then, different distribution candidates and modeling approaches are used with the collected data to identify probabilistic models for temperature dependents strength of steel and concrete. The proposed models are continuous probability distribution functions, with simple mathematical representations that are easy enough to arrange into systematic code for implementation in analytical and computational frameworks. Additionally, the proposed stochastic functions consider continuity in reliability appraisals during transition from room temperature to elevated temperatures. These models are applied to probabilistic evaluations of structural performance of three steel and two concrete columns, and the influence of the model choice is compared using fragility curves. Finally, the proposed probabilistic models, developed using different approaches, led to close results when characterizing the performance of structural members.
Probabilistic analysis is receiving increased attention from fire engineers, assessment bodies and researchers. It is however often unclear which probabilistic models are appropriate for the ...analysis. For example, in probabilistic structural fire engineering, the models used to describe the permanent and live loads differ widely between studies. Through a literature review, it is observed that these diverging load models are based on surveys conducted between 1893 and 1976 and that widely adopted assumptions, such as the rule for combining permanent and live loads into the total load effect, are commonly adopted based on precedent. The diverging current models however relate to mostly the same underlying datasets and basic methodologies. Differences can be attributed (largely) to specific assumptions in different background papers, which have become consolidated through repeated use in research papers and adoption in background documents to codes. By reviewing the studies underlying currently applied probabilistic load models in structural fire engineering, a consolidated probabilistic load model is proposed in this paper. It is concluded that the total load effect is ideally described by
K
E
·(
G
+
Q
), with
K
E
the model uncertainty for the load effect,
G
the permanent load, and
Q
the imposed load. The model uncertainty
K
E
can be described by a lognormal distribution with mean equal to unity and coefficient of variation (COV) of 0.10. The permanent load is preferably modelled by a normal distribution with mean equal to the nominal permanent load, and a COV which can either be assessed on a project specific basis, or can be set to 0.10 for a first assessment. For common occupancies (office, residential), the live load is preferably modelled by a Gamma distribution. The mean live load can be taken as 0.2 times the nominal, and the live load COV can be taken as 0.60 for large load areas (> 200 m
2
) and 0.95 for smaller load areas (< 100 m
2
). Comparison between the failure probabilities of steel and concrete columns subject to fire, considering the proposed consolidated model and two currently commonly used models, indicates that relative differences of the probability of failure can be in the order of 10%. Live load models for evacuation routes and warehouses require specific study and are outside the scope of the review.
Apart from mechanical actions, structural components in the construction industry may be subjected to a thermal gradient, causing (internally) restrained thermal expansion. These thermal loads can ...alter the mechanical response of components in a structural topology optimization procedure. Therefore, the influence of thermal loading should be considered in the sensitivity analysis to efficiently update the structural layout of material. In this paper, a density-based topology optimization procedure is developed for compliance minimization of structural components subjected to thermo-mechanical loads considering steady-state heat conduction and weak thermo-mechanical coupling. The adjoint method is employed to obtain the analytical sensitivities, taking into account the influence of the design-dependent temperature field and thermal properties. The proposed topology optimization procedure is demonstrated on the MBB problem, extended with thermal loading, to investigate the influence of the proposed sensitivities on the optimized results. Furthermore, the thermo-mechanical load ratio is quantitatively defined and its effect on the resulting topologies is studied. The results show that the thermo-mechanical load ratio significantly changes the topology of the optimized results. Finally, the topology optimization procedure is presented in an efficient 138-line MATLAB code and provided as supplementary material, serving as a basis for further research.
A simple framework for setting risk tolerability limits is proposed following a literature review of risk acceptance in fire safety engineering and a feedback round with international fire safety ...professionals. The framework provides practical guidance for the application of international fire safety guidance, such as the recently published UK guidance document on probabilistic risk assessment for the fire design of buildings, PD 7974-7:2019, which provides a state-of-the-art framework to assess adequate safety for complex fire engineering designs. However, the application of this guidance document is hindered by two main constraints: (1) PD7974-7:2019 requires risk tolerability limits to be set, but lacks guidance on defining them for a specific building project, and (2) no reference case studies are given that demonstrate the application of PRA methods to fire engineering design. In order to help fill this gap, a risk tolerability framework is developed and proposed herein. Finally, it is applied to a reference case study of a UK office building. Considering the developed framework, further research needs are identified. It is expected that the proposed risk tolerability framework and the presented reference case study can support the application of PRA to fire engineering design and ease stakeholder communication on setting risk tolerability limits.
Glass as a construction material has become indispensable and is still on the rise in the building industry. However, there is still a need for numerical models that can predict the strength of ...structural glass in different configurations. The complexity lies in the failure of glass elements largely driven by pre-existing microscopic surface flaws. These flaws are present over the entire glass surface, and the properties of each flaw vary. Therefore, the fracture strength of glass is described by a probability function and will depend on the size of the panels, the loading conditions and the flaw size distribution. This paper extends the strength prediction model of Osnes et al. with the model selection by the Akaike information criterion. This allows us to determine the most appropriate probability density function describing the glass panel strength. The analyses indicate that the most appropriate model is mainly affected by the number of flaws subjected to the maximum tensile stresses. When many flaws are loaded, the strength is better described by a normal or Weibull distribution. When few flaws are loaded, the distribution tends more towards a Gumbel distribution. A parameter study is performed to examine the most important and influencing parameters in the strength prediction model.
A machine learning algorithm was applied to predict the onset of flashover in archival experiments in a 1/5 scale ISO 13784‐1 enclosure constructed with sandwich panels. The experiments were ...performed to assess whether a small‐scale model could provide a better full‐scale correlation than the single burning item test. To predict the binary output, a regularized logistic regression model was chosen as ML environment, for which lasso‐regression significantly reduced the amount of variance at a negligible increase in bias. With the regularized model, it was possible to discern the predictive variables and determine the decision boundary. In addition, a methodology was put forward on how to use the to update the learning algorithm iteratively. As a result, it was shown how a learning algorithm can be used to facilitate ongoing experimentation. At first as a crude guideline, and in later stages, as an accurate prediction algorithm. It is foreseen that, by iteratively updating the algorithm, by compiling existing and new experiments in databases, and by applying fire safety knowledge, the final learned algorithm will be able to make accurate predictions for unseen samples and test conditions.
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